We derive new representations for the generalised Jacobian of a locally Lipschitz map between finite dimensional real Euclidean spaces as lower limit (i.e., inferior) classical derivative where it exists. The lead to significantly shorter proofs basic properties subgradient and including chain rule. establish that sequence maps converges given in L-topology—that is, weakest refinement sup norm ...

Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat the questions of the following type. Characterize which of the spaces from a given class support a semigroup of prescribed shape satisfying a given topological ergodic property. In particular, we characterize LBS-spaces (...

A space is called d-separable if it has a dense subset representable as the union of countably many discrete subsets. We answer several problems raised by V. V. Tkachuk by showing that (1) X is d-separable for every T1 space X; (2) if X is compact Hausdorff then X is d-separable; (3) there is a 0-dimensional T2 space X such that X2 is dseparable but X1 (and hence X) is not; (4) there is a 0-dim...

In 1968 Wilansky asked whether a separable normal topological group must be Lindelof. In [7] this question was answered in the negative, assuming CH, by constructing a hereditarily separable, normal group which is not Lindeliif. We give an example of a separable normal group which contains a closed subspace homeomorphic to an uncountable regular cardinal, in ZFC only. Of course we have to sacri...

Multi-view autostereoscopic displays can be considered as a kind of a multirate system due to the construction compromise between the number of different views and spatial resolution adopted for such displays. Images to be visualized on these displays are prone to aliasing errors. Careful antialiasing requires knowledge about the display frequency response, which is determined mainly by the vie...

In this paper we relate two topological invariants of a separable C*-algebras. The first is the shape invariant first studied by Effros and Kaminker [EK] and then developed further by Blackadar [B]. The second invariant is the isomorphism class of a C*-algebra in the asymptotic homotopy category A introduced by Connes and Higson [CH]. We prove that two separable C*-algebras are shape equivalent...

Classical results on weakly compactly generated (WCG) Banach spaces imply the existence of projectional resolutions of identity (PRI) and the existence of many projections on separable subspaces (SCP). We address the questions if these can be the only projections in a nonseparable WCG space, in the sense that there is a PRI (Pα : ω ≤ α ≤ λ) such that any projection is the sum of an operator in ...

Let X be a separable locally compact metrizable space and G a separable completely metrizable ANR topological group without isolated points. By C(X, G), we denote the topological group of all continuous maps f : X → G endowed with the Whitney (graph) topology and by Cc(X, G) the subgroup consisting of all maps with compact support. It is known that if X is compact and non-discrete then the spac...

For every metric space X, we deene a continuous poset BX such that X is home-omorphic to the set of maximal elements of BX with the relative Scott topology. The poset BX is a dcpo ii X is complete, and !-continuous ii X is separable. The computational model BX is used to give domain-theoretic proofs of Banach's xed point theorem and of two classical results of Hutchinson: on a complete metric s...

The notion of a <7-continuous matrix-valued positive definite distribution on 5/v(2a) x RM x G is introduced, where G is an abelian separable locally compact group and where Sp/(2a) is an open ball around zero in RA' with radius la > 0 . This notion generalizes that one of strongly continuous positive definite operator-valued functions. For these objects, a Bochner-type theorem gives a suitable...